The present invention relates to an apparatus and a method for measuring a quality measure of a clock signal that drives, for example, a microprocessor.
A jitter has traditionally been used as a measure for estimating quality of a clock signal of a microprocessor. Incidentally, there are two types of jitters, i.e., a period jitter and a timing jitter. As shown in FIG. 1A, in a jitter-free ideal clock signal, for example, an interval Tint between adjacent rising points is constant as indicated by a dotted line waveform, and in this case a period jitter is zero. In an actual clock signal, a rising edge fluctuates from an arrow toward leading side or trailing side, i.e., an interval Tint between adjacent rising points fluctuates, and this fluctuation of the interval is a period jitter. For example, in the case of a sine wave that does not have a rectangular waveform like a clock signal, a fluctuation of an interval Tint between zero crossing points is also a period jitter.
As shown in FIG. 1B, when a jitter-free square waveform is assumed to be a dashed line waveform, a deviation width xcex94xcfx86 of an actual rising point (solid line) from a normal rising point (dashed line) is a timing jitter in the case of a jittery square waveform.
A conventional measurement of a period jitter is performed by a time interval analyzer (hereinafter, this measuring method is referred to as a time interval method or a TIA method). This is shown in xe2x80x9cPhase Digitizing Sharpens Timing Measurementsxe2x80x9d, by David Chu, IEEE Spectrum, pp. 28-32, 1988, and xe2x80x9cTime Domain Analysis and Its Practical Application to the Measurement of Phase Noise and Jitterxe2x80x9d, by Lee D. Cosart et al., IEEE Trans. Instrum. Meas., vol. 46, pp. 1016-1019, 1997. This time interval method is a method in which zero crossing points of a signal under test are counted, an elapsed time is measured, and a time fluctuation between zero crossing points is obtained to obtain a period jitter. In addition, a root-mean-square value of the period jitters is obtained.
There is a method, as a conventional timing jitter measurement, in which a timing jitter is measured by measuring a phase noise-spectrum in frequency domain, and those spectrums are summed to estimate a root-mean-square value of timing jitters.
The inventors of the present invention have proposed a method of measuring a jitter as described below in an article entitled xe2x80x9cAn Application of An Instantaneous Phase Estimating Method to A Jitter Measurementxe2x80x9d in a technical report xe2x80x9cProboxe2x80x9d pp. 9-16 issued by Probo Editorial Room of ADVANTEST CORPORATION, Nov. 12, 1999. That is, as shown in FIG. 2, an analog clock waveform from a PLL circuit under test (Phase locked loop) 11 is converted into a digital clock signal xc(t) by an analog-digital converter 12, and the digital clock signal xc(t) is supplied to a Hilbert pair generator 14 acting as analytic signal transforming means 13, where the digital clock signal xc(t) is transformed into an analytic signal zc(t).
Now, a clock signal xc(t) is defined as follows.
xc(t)=Ac cos(2xcfx80fct+xcex8c+xcex94xcfx86(t))
The Ac and the fc are nominal values of amplitude and frequency of the clock signal respectively, the xcex8c is an initial phase angle, and the xcex94xcfx86(t) is a phase fluctuation that is called a phase noise.
The clock signal xc(t) is Hilbert-transformed by a Hilbert transformer 15 in the Hilbert pair generator 14 to obtain the following equation.
{circumflex over (x)}c(t)=H[xc(t)]=Ac sin(2xcfx80fct+xcex8c+xcex94xcfx86(t))
Then, an analytic signal zc(t) having xc(t) and {circumflex over (x)}c(t) as a real part and an imaginary part, respectively is obtained as follows.   "AutoLeftMatch"                                                        z              c                        ⁡                          (              t              )                                =                      xe2x80x83                    ⁢                                                    x                c                            ⁡                              (                t                )                                      +                                                            x                  ^                                c                            ⁡                              (                t                )                                                                                  =                      xe2x80x83                    ⁢                                    A              c                        ⁢                          cos              (                                                2                  ⁢                                      xe2x80x83                                    ⁢                  π                  ⁢                                      xe2x80x83                                    ⁢                                      f                    c                                    ⁢                  t                                +                                  θ                  c                                +                                  Δ                  ⁢                                      xe2x80x83                                    ⁢                  φ                  ⁢                                      xe2x80x83                                    ⁢                                      (                    t                    )                                                  +                                  j                  ⁢                                      xe2x80x83                                    ⁢                                      A                    c                                    ⁢                  sin                  ⁢                                      xe2x80x83                                    ⁢                                      (                                                                  2                        ⁢                                                  xe2x80x83                                                ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                                                  f                          c                                                ⁢                        t                                            +                                              θ                        c                                            +                                              Δ                        ⁢                                                  xe2x80x83                                                ⁢                        φ                        ⁢                                                  xe2x80x83                                                ⁢                                                  (                          t                          )                                                                                      )                                                                                          
From this analytic signal zc(t), an instantaneous phase "THgr"(t) of the clock signal xc(t) can be estimated by the instantaneous phase estimator 16 as follows.
"THgr"(T)=[2xcfx80fct+xcex8c+xcex94xcfx86(t)] mod 2xcfx80
A linear phase is removed from this instantaneous phase "THgr"(t) by a linear phase remover 17 to obtain a phase noise waveform xcex94xcfx86(t). That is, in the linear phase remover 17, a continuous phase converting part 18 applies a phase unwrap method to the instantaneous phase "THgr"(t) to obtain a continuous phase xcex8(t) as follows.
xcex8(t)=2xcfx80fct+xcex8c+xcex94xcfx86(t)
The phase unwrap method is shown in xe2x80x9cA New Phase Unwrapping Algorithmxe2x80x9d by Jose M. Tribolet, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-25, pp. 170-177, 1977 and in xe2x80x9cOn Frequency-Domain and Time-Domain Phase Unwrappingxe2x80x9d by Kuno P. Zimmermann, Proc. IEEE. vol. 75, pp. 519-520, 1987.
A linear phase [2xcfx80fct+xcex8c] of a continuous phase xcex8(t) is estimated by a linear phase evaluator 19 using a linear trend estimating method. This estimated linear phase [2xcfx80fct+xcex8c] is subtracted from the continuous phase xcex8(t) by a subtractor 21 to obtain a variable term xcex94xcfx86(t) of the instantaneous phase "THgr"(t), i.e., phase noise waveform as follows.
xcex8(t)=xcex94xcfx86(t)
The phase noise waveform xcex94xcfx86(t) thus obtained is inputted to a peak-to-peak detector 22, where a difference between the maximum peak value max (xcex94xcfx86(k)) and the minimum peak value min (xcex94xcfx86(1)) of the xcex94xcfx86(t) is calculated to obtain a peak value xcex94xcfx86pp of timing jitters as follows.       Δ    ⁢          xe2x80x83        ⁢          φ      pp        =                    max        k            ⁢              xe2x80x83            ⁢              (                  Δ          ⁢                      xe2x80x83                    ⁢          φ          ⁢                      xe2x80x83                    ⁢                      (            k            )                          )              -                  min        l            ⁢              xe2x80x83            ⁢              (                  Δ          ⁢                      xe2x80x83                    ⁢          φ          ⁢                      xe2x80x83                    ⁢                      (            1            )                          )            
In addition, the phase noise waveform xcex94xcfx86(t) is inputted to a root-mean-square detector 23, where a root-mean-square value of the phase noise waveform xcex94xcfx86(t) is calculated using following equation to obtain a root-mean-square value xcex94xcfx86RMS of timing jitters.       Δ    ⁢          xe2x80x83        ⁢          φ      RMS        =                    1        N            ⁢              xe2x80x83            ⁢                        ∑                      k            =            0                                N            -            1                          ⁢                  xe2x80x83                ⁢                  Δ          ⁢                      xe2x80x83                    ⁢                                    φ              2                        ⁡                          (              k              )                                          
A method for obtaining, in this manner, a peak value of timing jitters and/or a root-mean-square value of timing jitters from the phase noise waveform xcex94xcfx86(t) is called a xcex94xcfx86 method. According to the xcex94xcfx86 method, a jitter measurement can be performed in a test time of 100 millisecond order since measuring points are not limited to zero crossing points. Further, in FIG. 2, the analytic signal transforming means 13, the instantaneous phase estimator 16 and the linear phase remover 17 compose phase noise detecting means 25.
In the case of a jitter that each rising edge of a clock signal fluctuates in the same direction with substantially same quantity, a microprocessor driven by this clock signal is not influenced so much by the jitter. In a design of a PLL circuit that generates a clock signal, a correlation coefficient between rising edges of the clock signal is important. The correlation coefficient takes a vale of xe2x88x921 to +1. If, for example, this value is 0.6, it can be seen that the PLL circuit has room for improvement in correlation coefficient by 0.4. It can be deemed that a fluctuation between adjacent rising edges of a clock signal consists of a linear fluctuation (signal) in which a fluctuation of a following rising edge depends on a fluctuation of an immediately leading rising edge and a fluctuation (noise) in which a fluctuation of a following rising edge does not relate to a fluctuation of an immediately leading rising edge, whereby a signal to noise ratio of a fluctuation of a rising edge can be defined. Such a correlation coefficient or a signal to noise ratio can clarify more correctly than a root-mean-square value of period jitters or a root-mean-square value of timing jitters can as to whether or not, for example, a PLL circuit operates in the performance close to its theoretical limit. In addition, if such a correlation coefficient or a signal to noise ratio can be measured, those are effective for a test of a PLL circuit or the like. However, a method for measuring such a correlation coefficient or a signal to noise ratio between zero crossings of a signal, namely a quality measure of a phase noise waveform has not been proposed up to today.
It is an object of the present invention to provide an apparatus and a method that can measure a quality measure of a phase noise waveform.
According to a method of the present invention, an input signal is transformed into a complex analytic signal, and an instantaneous phase of the analytic signal is obtained. A linear phase is removed from the instantaneous phase to obtain a phase noise waveform, and a correlation coefficient and/or a signal to noise ratio of the phase noise waveform, i.e., a quality measure of the phase noise waveform is obtained from the phase noise waveform. That is, according to the present invention, a quality measure is obtained by the aforementioned xcex94xcfx86 method.
A signal to noise ration is obtained from the correlation coefficient. There will be explained below a principle for obtaining a correlation coefficient, and also for obtaining a signal to noise ratio from the correlation coefficient.
A correlation coefficient xcfx81tt(T) between adjacent zero crossing points nT and (n+1)T of an instantaneous timing jitter {xcex94xcfx86(nT)} (T is a period of a clock signal) is obtained as follows.
A period jitter Jp is obtained from a difference between two timing jitters xcex94xcfx86(nT) and xcex94xcfx86((n+1)T) of an input signal each being spaced apart from one another by a period T. A variance "sgr"p2(T) of this period jitter Jp is obtained by the following equation as an expected value of the period jitter Jp.   "AutoLeftMatch"                                                        σ              p              2                        ⁡                          (              T              )                                =                      E            ⁡                          (                                                {                                                            Δ                      ⁢                                              xe2x80x83                                            ⁢                      φ                      ⁢                                              xe2x80x83                                            ⁢                                              (                                                                              (                                                          n                              +                              1                                                        )                                                    ⁢                          T                                                )                                                              -                                          Δ                      ⁢                                              xe2x80x83                                            ⁢                                              φ                        ⁡                                                  (                          T                          )                                                                                                      }                                2                            )                                                                    =                                    E              ⁡                              (                                                      {                                          Δ                      ⁢                                              xe2x80x83                                            ⁢                      φ                      ⁢                                              xe2x80x83                                            ⁢                                              (                                                                              (                                                          n                              +                              1                                                        )                                                    ⁢                          T                                                )                                                              }                                    2                                )                                      -                          2              ⁢                              xe2x80x83                            ⁢                              E                ⁡                                  (                                      Δ                    ⁢                                          xe2x80x83                                        ⁢                    φ                    ⁢                                          xe2x80x83                                        ⁢                                          (                                                                        (                                                      n                            +                            1                                                    )                                                ⁢                        T                                            )                                        ⁢                                          xe2x80x83                                        ⁢                    Δ                    ⁢                                          xe2x80x83                                        ⁢                                          φ                      ⁡                                              (                        T                        )                                                                              )                                                      +                          E              ⁡                              (                                                      {                                          Δ                      ⁢                                              xe2x80x83                                            ⁢                      φ                      ⁢                                              xe2x80x83                                            ⁢                                              (                        T                        )                                                              }                                    2                                )                                                                                  =                                    σ              t              2                        -                          2              ⁢                              xe2x80x83                            ⁢                                                E                  ⁡                                      (                                          Δ                      ⁢                                              xe2x80x83                                            ⁢                      φ                      ⁢                                              xe2x80x83                                            ⁢                                              (                                                                              (                                                          n                              +                              1                                                        )                                                    ⁢                          T                                                )                                            ⁢                                              xe2x80x83                                            ⁢                      Δ                      ⁢                                              xe2x80x83                                            ⁢                                              φ                        ⁡                                                  (                          T                          )                                                                                      )                                                                                        σ                    t                                    ⁢                                      σ                    t                                                              ⁢                              xe2x80x83                            ⁢                              σ                t                            ⁢                              σ                t                                      +                          σ              t              2                                          
In this case, "sgr"t2 is a variance of timing jitter xcex94xcfx86(T).
From equations (7-6) and (7-8) in page 150 of xe2x80x9cProbability, Random Variables, and Stochastic Processesxe2x80x9d by A. Papoulis, 2nd Edition, McGraw-Hill Book Company, and from a fact that each of xcex94xcfx86(nT) and xcex94xcfx86((n+1)T) is a deviation from an average value,       E    ⁡          (              Δ        ⁢                  xe2x80x83                ⁢        φ        ⁢                  xe2x80x83                ⁢                  (                                    (                              n                +                1                            )                        ⁢            T                    )                ⁢                  xe2x80x83                ⁢        Δ        ⁢                  xe2x80x83                ⁢        φ        ⁢                  xe2x80x83                ⁢                  (          T          )                    )                  σ      t        ⁢          σ      t      
is a correlation coefficient xcfx81tt between xcex94xcfx86(nT) and xcex94xcfx86((n+1)T). Therefore, the following equation is obtained.
"sgr"p2(T)=2(1xe2x88x92xcfx81tt(T))"sgr"t2(T)xe2x80x83xe2x80x83(1)
This can be re-written as follows.                                           ρ            tt                    ⁡                      (            T            )                          =                  1          -                                                    σ                p                2                            ⁡                              (                T                )                                                    2              ⁢                              xe2x80x83                            ⁢                                                σ                  t                  2                                ⁡                                  (                  T                  )                                                                                        (        2        )            
In the above equation, "sgr"p(T) is a root-mean-square value of period jitters Jp, and "sgr"t,(T) is a root-mean-square value of timing jitters xcex94xcfx86(T).
Alternatively, a correlation coefficient "sgr"tt(T) can be obtained, from the definition of a correlation coefficient, by the following equation using a timing jitter {xcex94xcfx86(nT)}.                                           ρ            tt                    ⁡                      (            T            )                          =                                            σ              tt                                                      σ                t                            ⁢                              σ                t                                              =                                                    ∑                i                            ⁢                              xe2x80x83                            ⁢                                                {                                                            Δ                      ⁢                                              xe2x80x83                                            ⁢                                              φ                        ⁡                                                  (                          iT                          )                                                                                      -                                          Δ                      ⁢                                              xe2x80x83                                            ⁢                                              φ                        xe2x80x2                                                                              }                                ⁢                                  {                                                            Δ                      ⁢                                              xe2x80x83                                            ⁢                                              φ                        ⁡                                                  (                                                                                    (                                                              i                                +                                1                                                            )                                                        ⁢                            T                                                    )                                                                                      -                                          Δ                      ⁢                                              xe2x80x83                                            ⁢                                              φ                        xe2x80x2                                                                              }                                                                                    ∑                i                            ⁢                              xe2x80x83                            ⁢                                                (                                                            Δ                      ⁢                                              xe2x80x83                                            ⁢                                              φ                        ⁡                                                  (                          iT                          )                                                                                      -                                          Δ                      ⁢                                              xe2x80x83                                            ⁢                                              φ                        xe2x80x2                                                                              )                                2                                                                        (        3        )                                =                                                            ∑                i                            ⁢                              xe2x80x83                            ⁢                              Δ                ⁢                                  xe2x80x83                                ⁢                                  φ                  ⁡                                      (                    iT                    )                                                  ⁢                Δ                ⁢                                  xe2x80x83                                ⁢                φ                ⁢                                  xe2x80x83                                ⁢                                  (                                                            (                                              i                        +                        1                                            )                                        ⁢                    T                                    )                                                      -                          Δ              ⁢                              xe2x80x83                            ⁢                              φ                                  xe2x80x2                  ⁢                                      xe2x80x83                                    ⁢                  2                                                                                        ∑              i                        ⁢                          xe2x80x83                        ⁢                                          (                                                      Δ                    ⁢                                          xe2x80x83                                        ⁢                                          φ                      ⁡                                              (                        iT                        )                                                                              -                                      Δ                    ⁢                                          xe2x80x83                                        ⁢                                          φ                      xe2x80x2                                                                      )                            2                                                          (        4        )            
In the above equation, xcex94xcfx86xe2x80x2 is an average value of the xcex94xcfx86(nT).
Further, since xcex94xcfx86(iT) itself is a deviation from the linearity according to the definition of a timing jitter, xcex94xcfx86xe2x80x2 is zero and hence this may be omitted from the equations (3) and (4). In addition, since xcex94xcfx86xe2x80x2/"sgr"t is a small value such as xcex94xcfx86xe2x80x2/"sgr"txe2x89xa1{fraction (6/1000)} from an experiment, xcex94xcfx86xe2x80x2 may be omitted from the equations (3) and (4).
A timing jitter variance "sgr"tt2 of xcex94xcfx86((n+1)T) that fluctuates against a timing jitter xcex94xcfx86(nT) based on only a linear relationship with its fluctuation can be expressed by the following equation.
"sgr"tt2=xcfx81tt2"sgr"t(n+1)2xe2x80x83xe2x80x83(5)
A timing jitter variance "sgr"t,n2 of xcex94xcfx86((n+1)T) that fluctuates against a timing jitter xcex94xcfx86(nT) based on other noises including a nonlinear relationship with its fluctuation can be expressed by the following equation.
xe2x80x83"sgr"t,n=(1xe2x88x92xcfx81tt2)"sgr"t(n+1)2xe2x80x83xe2x80x83(6)
The equations (5) and (6) are shown in equations (3.10) and (3.11) in page 43-47 of xe2x80x9cEngineering Applications of Correlation and Spectral Analysisxe2x80x9d by J. S. Bendat and A. G. Piersol, John Wiley and Sons, 1980.
From the equations (5) and (6), a ratio of a linear fluctuation (signal component) of a timing jitter {xcex94xcfx86((n+1)T)} based on a fluctuation of xcex94xcfx86(nT) to a fluctuation (noise) not related to a fluctuation of the xcex94xcfx86(nT), i.e., a noise to signal ratio SNRt can be obtained by the following equation.                               SNR          t                =                                            σ                              t                ,                t                            2                                      σ                              t                ,                n                            2                                =                                    ρ              tt              2                                      1              -                              ρ                tt                2                                                                        (        7        )            
Incidentally, if a timing jitter variance "sgr"t is large, 1/SNRt is also large, and if a timing jitter variance "sgr"t is small, 1/SNRt is also small. That is, "sgr"t is proportional to 1/SNRt. Therefore, if "sgr"t2 in the right side of the equation (1) is multiplied by 1/SNRt as a proportional coefficient, and the both sides are extracted and then the both sides are divided by T, the following equations can be obtained.                                           σ            p                    T                ⁢                  xe2x80x83                ∝                                            2              ⁢                              (                                  1                  -                                      ρ                    tt                                                  )                                              ·                                                                      σ                  t                  2                                                  SNR                  t                                                      T                                              (        8        )            
As mentioned above, by obtaining a period jitter variance "sgr"p and a timing jitter variance "sgr"t, a correlation coefficient xcfx81tt of a timing jitter, i.e., a phase noise waveform xcex94xcfx86(t) can be obtained. In addition, a correlation coefficient xcfx81tt can be obtained from the equations (3) and (4) using a timing jitter xcex94xcfx86(nT). Furthermore, a signal to noise ratio SNrt of a phase noise waveform xcex94xcfx86(t) can be obtained from the equation (7) using the correlation coefficient xcfx81tt.
In the present invention, a quality measure such as a correlation coefficient xcfx81tt or a signal to noise ratio SNRt is obtained by such a method using the xcex94xcfx86(t).